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Alheydis Geiger

Research interests

My main focus is the area of tropical geometry. In particular in its connections to algebraic geometry, enumerative geometry, combinatorics and polyhedral geometry, matroid theory, and its computational aspects.

Scientist

Alheydis Geiger

Tropical Algebraic Geometry
Email
Nonlinear Algebra Mathematical Software MiS Profile
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Publications

inJournal
2024
Alheydis Geiger et al.

Computing tropical bitangents to smooth quartic curves in \(polymake\)

In: Journal of symbolic computation

BibTex

 DOI: 10.1016/j.jsc.2023.102225 ArXiv: 2112.04447
Preprint
2023
Nick Early et al.

Positive del Pezzo geometry

BibTex

 ArXiv: 2306.13604 Code: mathrepo.mis.mpg.de
inJournal
2023
Alheydis Geiger et al.

A tropical count of real bitangents to plane quartic curves

In: The electronic journal of combinatorics

BibTex

 DOI: 10.37236/11099 ArXiv: 2112.04433
Preprint
2023
Alheydis Geiger et al.

Graph curve matroids

BibTex

 ArXiv: 2311.08332 Code: mathrepo.mis.mpg.de
inJournal
2023
Alheydis Geiger et al.

Self-dual matroids from canonical curves

In: Experimental mathematics

BibTex

 DOI: 10.1080/10586458.2023.2239282 ArXiv: 2212.05910 Code: mathrepo.mis.mpg.de
inJournal
2020
Madeline Brandt et al.

A tropical count of binodal cubic surfaces

In: Le Matematiche

BibTex

 DOI: 10.4418/2020.75.2.14 ArXiv: 1909.09105
All Personal Publications
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Curriculum vitae

Since August 2023 I am post-doc in the math software group lead by Michael Joswig at MPI MiS in Leipzig.

From July 2022-August 2023 I was a post-doctoral researcher in the Non-Linear Algebra Group by Bernd Sturmfels at MPI MiS in Leipzig.

Studies

  • July 2022 PhD (Universität Tübingen), "Tropical Geometric Counting Problems", supervisor Prof. Hannah Markwig
  • March 2020 Master of Science (Universität Tübingen), Masterthesis: Tropical Cubic Surfaces - Enumeration and Lines, supervisor: Prof. Hannah Markwig.
  • Sep. 2018 Master of Science (University of Warwick), Masterthesis: Realisability of infinite families of tropical lines on general smooth cubic surfaces, supervisor: Prof. Diane Maclagan
  • Oct. 2016 Bachelor of Science (Universität Tübingen)

Conferences, Seminars and Talks

  • 16.-18.10.2023, Chow Lectures, preparatory class: "M-convex functions, (valuated) matroids and Lorentzian polynomials", MPI MiS Leipzig
  • 25.-28.9.2023, DMV Meeting, Ilmenau, Talk: "Positive del Pezzo Geometry"
  • 7.-11.8.2023, Algebraic, Tropical, and Logarithmic workshop, Banff, Talk: "Self-dual matroids from canonical curves"
  • 10.-14.7.2023, SIAM AG, Eindhoven, Talk: "Positive del Pezzo Geometry" in the Minisymposium "Real Algebraic Geometry"
  • 28.-29.6.2023, 24 Hours of Combinatorial Synergies, Magdeburg, Talk: "Positive del Pezzo Geometry"
  • 15.6.2023, Joint Algebra Seminar, Aachen (online), Talk: "Positive del Pezzo Geometry"
  • 15.6.2023, Oberseminar Algebra, Chemnitz, Talk: "Positive del Pezzo Geometry"
  • 31.5.-2.6.2023, Computeralgebra Fachschaftstagung, Hannover, Talk: "Self-dual matroids from canonical curves - computational challenges"
  • 29.-31.3.2023, Regional Workshop in Algebraic Geometry, Jena, Talk: "Self dual matroids from canonical curves"
  • 17.2.2023, LMS workshop on Tropical Mathematics, Talk: "Self-Duality in Tropical Geometry"
  • 24.-25.11.2022, MOM workshop on MaRDI, OSCAR and MATHREPO, Talk: "Self-dual matroids from canonical curves - computational challenges"
  • 22.11.2022,  Algebra Seminar Osnabrück, Talk: "A tropical count of real bitangents to plane quartic curves"
  • 14.-18.11.2022, Newton-Okunkov Bodies & Tropical Geometry, Frankfurt, Talk: "Self dual matroids from canonical curves"
  • 7.11.2022, Moduli Day, MPI MiS Leipzig, Talk: "Self dual matroids from canonical curves"
  • 01.08.-05.08.2022 "Young Researchers Conference in Non-Archimedean and Tropical Geometry", Regensburg, Introductory Lecture: "Applications of tropical geometry"
  • 20.06.-24-06.2022 "MEGA", Kraków, Poland
  • 15.03.-17.03.2022, "Lectures on Theta - Replacement", MPI MiS Leipzig
  • 29.11.-1.12.2021 „Women in Algebra and Symbolic Computation II“, SFB-TRR 195, Bad Dürkheim, Talk: „Towards counting tropical binodal surfaces“
  • 24.-30.10.2021, Oberwolfach Seminar: Tropical Curves, Logarithmic Structures, and Enumerative Geometry
  • 13.-16.09.2021, Fifth annual conference of the SFB-TRR 195, RWTH Aachen, Talk: "Counting tropical binodal surfaces" and Joint Talk: "A tropical proof of Plücker's Theorem" with Marta Panizzut
  • 16.08.-20.08.2021 SIAM Conference on Algebraic Geometry, Talk: "Deformations of Bitangent Classes of Tropical Quartic Curves"
  • 07.06.-11.06.2021 MEGA Conference, University Tromsø - The Artic University of Norway, Online.
  • 11.05.2021 Seminar Talk: "Deformations of Bitangent Classes of Tropical Quartic Curves", Tübingen.
  • 22.01.2021 "TGIZ-Tropical geometry in Zoom", Goethe Universität Frankfurt am Main, Talk: "Deformations of bitangent classes of tropical quartic curves"
  • 13.07.-16.07.2020 "International Congress on Mathematical Software", TU Braunschweig, Online Conference, Talk: "Tropical Algebraic Geometry - A tropical count of binodal cubic surfaces"
  • 09.12.-11.12.2019 „Women in Algebra and Symbolic Computation“, SFB-TRR 195, Bad Dürkheim, Talk: „Tropical Cubic Surfaces“
  • 29.07.-02.08.2019 „Young Researchers Conference in Non-Archimedean and Tropical Geometry“, Universität Regensburg, Talk: „Relative Realisability of infinite families of tropical lines on general smooth tropical cubic surfaces“
  • 08.05.2019 Researchseminar, TU Berlin, Talk: "Realisability of infinite families of tropical lines on general smooth cubic surfaces" 

Workshops and more

Summer Schools

  • 05.09.-09.09.2022 "Combinatorial Methods in Algebraic Geometry", Cambridge, England
  • 23.05.-27.05.2022 "International Summer School on Tropical Geometry", Valladolid, Spain
  • 06.09.-10.09.2021 "Computeralgebra", RWTH Aachen
  • 23.08.-27.08.2021 "Tropical homology and Hodge theory", online format
  • 26.07.-06.08.2021 "Combinatorial Algebraic Geometry",LMs-Bath Symposium, University of Bath, virtual format
  • 28.06.-02.07.2021 "Tropical Moduli Spaces", EWM/EMS Mittag Leffler summer school, virtual format
  • 06.2020-07.2020 "Algebraic and Tropical Online Meetings"
  • 03.06.2019-07.06.2019 „New Perspectives in Gromov-Witten Theory“, Summer School at Sorbonne Université, Paris

Teaching

  • Summersemester 2023: Introduction to tropical geometry
  • winter term 2021/2022: teaching assistant for "Commutative Algebra", Lecturer: Thomas Markwig
  • Since winter term 2020/21: Conductor of the training for mentors in the mentoring programm for first year students (in the winter term 2020/21 together with Sophia Jahns, since summer term 2021 single-handedly)
  • winter term 2020/2021: teaching assistant for "Introduction to algebraic geometry and commutative algebra", Lecturer: Hannah Markwig
  • summer term 2020: teaching assistant for "Algebra", Lecturer: Hannah Markwig
  • 2014-2020: support class teacher for different lectures